Novel Slope Source Term Treatment for Preservation of Quiescent Steady States in Shallow Water Flows

Abstract

This paper proposes a robust method for modeling shallow-water flows and near shore tsunami propagation, applicable for both simple and complex geometries with uneven beds. The novel aspect of the model includes the introduction of a new method for slope source terms treatment to preserve quiescent equilibrium over uneven topographies, applicable to both structured and unstructured mesh systems with equal accuracy. Our model is based on the Godunov-type finite volume numerical approximation. Second-order spatial and temporal accuracy is achieved through high resolution gradient reconstruction and the predictor-corrector method, respectively. The approximate Riemann solver of Harten, Lax, and van Leer with contact wave restoration (HLLC) is used to compute fluxes. Comparisons of the model's results with analytical, experimental, and published numerical solutions show that the proposed method is capable of accurately predicting experimental and real-time tsunami propagation/inundation, and dam-break flows over varying topographies.

Fast Simulation of Large-Scale Floods Based on GPU Parallel Computing

“…In recent years, the shallow water model has been widely researched and used for flood simulations [1][2][3][4][5][6]. Song et al [1] proposed a robust and well-balanced finite volume model by using a new formulation of shallow water equations.…”

“…Liu et al [4] proposed a coupled 1D-2D hydrodynamic model for flood risk mapping. Rehman and Cho [5] proposed a robust method of slope source term treatment for modeling shallow-water flows and near-shore tsunami propagation. Kvocka et al [6] determined a threshold value of the bottom slope for using the flood inundation model with shock-capturing algorithms.…”